Answer the following questions based on the information given below.
Raycasting is a technique used in the creation of computer games. The basic idea of raycasting is as follows: the map is a 2D square grid. Using rays generated from an object, this 2D map can be transformed into a 3D perspective. One of the methods involves sending out a ray from the player's location. To determine how far he/she is from a wall or an obstacle, the distance between the player's coordinates and the coordinate of the wall is calculated. If the player is near the obstacle, it looks larger and vice-versa.
Shown below is a game, Wolf 3D, which was created using raycasting.

Riju wants to create an online snooker game using raycasting. The game in the creation stage on a coordinate map is shown below.

The snooker table has six pockets `(P_1, P_2, P_3, P4, P_5 and P_6)` and he has shown three balls -white (W), red (R) and green (G) on the table. The objective of the game is to use the white ball to hit the coloured balls into the pockets using a cue stick.
i) How much distance will a ray travel if sent from the green ball to the nearest pocket? Show your work.
ii) Riju wants to place a yellow ball at the midpoint of the line connecting the white and green balls.
Find the coordinates of the point at which he should place the yellow ball. Show your steps.
iii) Riju is running a trial on his game. He struck the white ball in a way that it rebound off the rail (line connecting `P_4` and `P_6`) and went into the pocket `P_2`.
♦ After the rebound, the ball crossed the x-axis at point `X (frac {2}{7}, 0)` on the way to the pocket.
♦ The ratio of the distance between the rail and point X and the distance between point X and the pocket was 3:4.
Find the coordinates of the point at which the ball struck the rail. Show your steps.
OR
Riju wants to hit a blue ball placed at `(-1, -3)` into pocket `P_5` along a straight path. Would the red ball lie on the straight path between the blue ball and `P_5`? Justify your answer.